$4\mathrm{.}26$ Consider the Turing machine $P=\{q_0(B)1q_1,q_{0}1R{q}_0,q_{1}BR{q}_2,q_{1}1(L)q_1\}.$

fine $g(x,y)=0$ if the machine $P,$ when started on a tape that is blank except

$x-$many consecutive $1\text{'}$s and with the head under the leftmost $1,$ has halted a

step $y.$ Otherwise, $g(x,y)=1.$ Find $f(x)=y[g(x,y)=0]$ for